An asymmetric color image optical encryption method based on generalized singular value decomposition

Abstract

The application discloses a kind of asymmetric color image optical encryption methods based on generalized singular value decomposition, including encryption process and decryption process, encryption process: asymmetric optical encryption system of color image, the technical scheme adopted is, in encryption system, a kind of double random phase encoding encryption scheme based on generalized singular value decomposition is designed, color image is first encoded into complex matrix, the complex matrix obtained is modulated with phase plate by generalized singular value decomposition, then encryption is carried out in optical Fourier transform domain using phase truncation technique, finally the ciphertext is received by charge coupled device.The application mainly aims at the problem that existing asymmetric encryption system based on phase truncation cannot resist special attack, a kind of modulation method based on generalized singular value decomposition is designed to image and random phase plate, the encryption algorithm can realize color image encryption, effectively resist shear attack, noise attack, chosen-plaintext attack and special attack.

Description

Technical Field

[0001] This invention relates to an asymmetric encryption method, specifically an asymmetric color image optical encryption method based on generalized singular value decomposition, belonging to the fields of optical encryption technology and information security. Background Technology

[0002] As a primary means of protecting image information security, image encryption technology has been extensively studied in recent years and has become one of the research hotspots in the field of image information security. Image encryption involves scrambling the pixel positions or sizes of an image to encode meaningful image information into meaningless gibberish, thereby protecting the image's information security. Based on the technical means employed, image encryption methods can be divided into digital image encryption methods and optical image encryption methods. Among them, optical image encryption has advantages such as high speed, large capacity, parallelism, and the ability to quickly perform convolution and correlation operations. Optical image encryption methods are generally classified as symmetric and asymmetric. In symmetric encryption systems, the encryption system is vulnerable to attacks such as chosen plaintext and known plaintext attacks due to its linearity or symmetry.

[0003] To improve the security of encryption systems, researchers have proposed introducing nonlinear operations or constructing asymmetric encryption systems. Phase truncation, as one of the most representative techniques in the field of asymmetric encryption, has been extensively studied in image encryption in recent years. The main advantage of phase-truncation-based asymmetric encryption systems is their resistance to chosen-plaintext attacks, but they are not resistant to special attacks. Therefore, the development, design, and research of asymmetric image encryption systems have become a focus and important research direction in the field of information security. Proposing a secure and effective asymmetric optical encryption algorithm will have a positive and significant impact on promoting the progress of image encryption research. Summary of the Invention

[0004] The purpose of this invention is to provide an asymmetric color image optical encryption method based on generalized singular value decomposition to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an asymmetric color image optical encryption method based on generalized singular value decomposition, comprising an encryption process and a decryption process.

[0006] 1) Encryption process: The color image is first encoded into a complex matrix. The obtained complex matrix is ​​modulated with a phase plate through generalized singular value decomposition. Then, the phase truncation technique is used to encrypt the image in the optical Fourier transform domain. Finally, the ciphertext is received through a charge-coupled device. The specific decryption process is as follows.

[0007] 2) Decryption process: First, the matrix is ​​recovered using the ciphertext and private key. Then, the matrix is ​​Fourier transformed to obtain the matrix. Finally, the matrix is ​​recovered according to the principle of generalized singular value decomposition. The blue component of the original image and the matrix are extracted from the imaginary and real parts of the complex matrix.

[0008] The matrix is ​​then recovered using the private key, and an inverse Fourier transform is performed on the matrix to obtain the next matrix. The complex matrix is ​​then recovered based on the principle of generalized singular value decomposition. The real and imaginary parts are extracted to recover the red and green components of the original image. The original image can then be recovered from the extracted blue, red, and green components.

[0009] Preferably, the encryption process of the encryption algorithm is described as follows:

[0010] Step 1: Assume the image needs to be encrypted. For a picture of size For a pixel-based color image, the three color components of the image are first normalized. , , These represent the normalized red, green, and blue color components, respectively; then, the red and green components are used as the real and imaginary parts of the complex number, respectively, to encode the first complex matrix:

[0011]

[0012] Step 2: Combine the first complex matrix with the random phase mask Generalized singular value decomposition yields two unitary matrices. and A square array and two non-negative diagonal matrices and :

[0013]

[0014] Step 3: For non-negative diagonal matrices Perform a Fourier transform to obtain the matrix in the frequency domain. :

[0015]

[0016] Step 4: In the frequency domain, for Perform phase truncation and amplitude truncation:

[0017]

[0018]

[0019] in, and These respectively indicate phase truncation and amplitude truncation.

[0020] Step 5: Amplitude information obtained after phase truncation The blue component of the image is encoded as the real and imaginary parts of the complex number, respectively, into a second complex matrix. :

[0021]

[0022] Step 6: For the second complex matrix and random phase mask Perform generalized singular value decomposition:

[0023]

[0024] Step 7: For non-negative diagonal matrices The spatial domain image is obtained by performing an inverse Fourier transform. :

[0025]

[0026] Step 8: Perform phase and amplitude truncation on it in the spatial domain:

[0027]

[0028]

[0029] Step 9: Amplitude information obtained after phase truncation Transmitted as encrypted text;

[0030] Two random phase masks were used in the encryption process. and Two square matrices generated during the encryption process and Two unitary matrices and The phase information matrix obtained by two amplitude truncations and Both are used as decryption keys to decrypt the image.

[0031] Preferably, the decryption process of the encryption algorithm is described as follows:

[0032] Step 1: Decryption begins with the ciphertext. and private key Recovery Matrix :

[0033]

[0034] in Represents matrix dot product;

[0035] Step 2: For the matrix The matrix is ​​obtained by performing a Fourier transform. :

[0036]

[0037] Step 3: Recover the second complex matrix based on the principle of generalized singular value decomposition. :

[0038]

[0039] in, Representation matrix The conjugate transpose of ;

[0040] Step 4: From the second complex matrix Extracting the blue component from the imaginary and real parts of the original image sum matrix :

[0041]

[0042]

[0043] here, This indicates extracting the imaginary part of a complex number. This indicates extracting the real part of a complex number;

[0044] Step 5: Using the private key Recovery Matrix :

[0045]

[0046] Step 6: For the matrix The matrix is ​​obtained by performing an inverse Fourier transform. :

[0047]

[0048] Step 7: Recover the complex matrix based on the principle of generalized singular value decomposition. :

[0049]

[0050] Step 8: Extracting the real and imaginary parts will recover the red component of the original image. and green components :

[0051]

[0052]

[0053] The encryption system uses a random phase mask. and Encryption, using , , , , and The encrypted text is decrypted because the encryption key and the decryption key are different, thus achieving asymmetric encryption. In addition, the encryption system can also be used to encrypt three grayscale images simultaneously. By using three grayscale images instead of the three color components of a color image for encryption, three grayscale images can be encrypted simultaneously.

[0054] Preferably, the specific steps of the special attack based on iterative recovery designed according to the present invention are detailed as follows:

[0055] matrix , , The first generation generated by the amplitude-phase retrieval algorithm The predicted values ​​represent the red, green, and blue components of the image, respectively. When performing the first iteration, its initial value is set to 1; matrix This is encrypted text used to constrain the recovered image;

[0056] Step 1: First, perform generalized singular value decomposition on the image complex matrix and the random phase mask:

[0057]

[0058] Step 2: Obtain the diagonal matrix from the generalized singular value decomposition. The key is obtained by performing phase-truncation and amplitude-truncation Fourier transforms. and the middle ciphertext :

[0059]

[0060]

[0061] Step 3: Convert the matrix The predicted value of the blue component of the original image The real and imaginary parts of the complex number are encoded into a complex matrix, respectively. Then, this complex matrix and a random phase mask are used... Perform generalized singular value decomposition:

[0062]

[0063] Step 4: Divide the diagonal matrix The key is obtained by performing an amplitude-trunculated inverse Fourier transform. :

[0064]

[0065] Step 5: Through ciphertext Generate the first Predicted blue component values ​​of the original image in the next iteration:

[0066]

[0067] Step 6: Generate intermediate matrix :

[0068]

[0069] Step 7: Generate predicted values ​​for the color matrix of the original image based on the previously generated key:

[0070]

[0071] Step 8: Extracting the real and imaginary parts separately yields the predicted values ​​of the red and green components of the original image.

[0072]

[0073] .

[0074] Compared with the prior art, the beneficial effects of the present invention are:

[0075] Compared to previously proposed color image encryption algorithms, this invention primarily focuses on the security against specific attacks. It proposes an encryption module comprised of an asymmetric optical encryption system and designs an asymmetric color image optical encryption method based on generalized singular value decomposition. Its advantages are:

[0076] This method can encrypt both color images and multiple grayscale images;

[0077] This encryption method can resist a certain degree of shearing and noise attacks;

[0078] Compared to symmetric systems based on double random phase coding, the method proposed in this invention can resist chosen-plaintext attacks;

[0079] Compared to widely used asymmetric encryption systems based on phase truncation, the method proposed in this invention can resist special attacks;

[0080] The modulation method for color images and random phase plates based on generalized singular value decomposition proposed in this invention can be extended to other optical transform domains. Attached Figure Description

[0081] Figure 1 A schematic diagram of the encryption principle provided by this invention;

[0082] Figure 2 A schematic diagram illustrating the decryption principle provided by this invention;

[0083] Figure 3 Here is a sample of the original color image to be encrypted, the encrypted result, and the decrypted result:

[0084] (a) is the original color image;

[0085] (b) is the encrypted result;

[0086] (c) is the decrypted result;

[0087] Figure 4 Histogram distributions of the original and encrypted images:

[0088] (a) shows the histogram distribution of the original image;

[0089] (b) is the histogram distribution of the encrypted image;

[0090] Figure 5 For different key cases from Figure 3 The image decrypted in (b) is shown in the figure:

[0091] (a) is the decryption result when key X1 is incorrect;

[0092] (b) is the decryption result when the key X2 is incorrect;

[0093] (c) is the decryption result when key p1 is incorrect;

[0094] (d) is the decryption result when key p2 is incorrect;

[0095] (e) is the decryption result when key U1 is incorrect;

[0096] (f) is the decryption result when key U2 is incorrect;

[0097] Figure 6 Decrypted image under conditions of shearing attack:

[0098] (a) is an encrypted image subjected to a 1 / 64 cut attack;

[0099] (b) is the result decrypted from 6(a);

[0100] (c) is an encrypted image subjected to a 1 / 16 cut attack;

[0101] (d) is the result decrypted from 6(c);

[0102] Figure 7 Decrypted image under Gaussian noise attack:

[0103] (a) is the decryption result when subjected to 0.1 times Gaussian noise attack;

[0104] (b) is the decryption result when subjected to 0.2 times Gaussian noise;

[0105] (c) is the decryption result when subjected to 0.5 times Gaussian noise attack;

[0106] Figure 8 For pseudo-plaintext images and decrypted images under chosen-plaintext attacks:

[0107] (a) is a pseudo-plaintext image;

[0108] (b) is the decryption result obtained using the pseudo-key;

[0109] Figure 9 This is a schematic diagram illustrating the specific attack principle designed to counter this invention;

[0110] Figure 10 The results of a specific attack against the encryption method designed in this invention are as follows:

[0111] (a) is the image recovered after 100 iterations;

[0112] (b) is a graph showing the correlation coefficient between the decrypted image recovered through a special attack and the original image as a function of the number of iterations.

[0113] The components represented by each number in the diagram are listed below:

[0114] Figure 1 middle: , , These represent the normalized red, green, and blue color components, respectively. Represents the first random phase plate; Represent and The two unitary matrices obtained by generalized singular value decomposition and A square array and two non-negative diagonal matrices and ; Represents the Fourier transform; Represents a non-negative diagonal matrix Perform a Fourier transform to obtain the matrix in the frequency domain. ; and These represent phase truncation and amplitude truncation operations, respectively. The phase information matrix obtained by amplitude truncation can be used as a private key for decryption; This represents the amplitude information obtained after phase truncation. Represents the second random phase plate; Represent and The two unitary matrices obtained by generalized singular value decomposition and A square array and two non-negative diagonal matrices and ; Represents the inverse Fourier transform; Represents a non-negative diagonal matrix The spatial domain image is obtained by performing an inverse Fourier transform; The phase information matrix obtained by amplitude truncation can be used as a private key for decryption; The amplitude information obtained after phase truncation can be transmitted as ciphertext.

[0115] Figure 9 Chinese: Matrix , , The first generation generated by the amplitude-phase retrieval algorithm The predicted values ​​represent the red, green, and blue components of the image, respectively. When performing the first iteration, its initial value is set to 1; matrix This is encrypted text used to constrain the recovered image; They represent the complex matrix of the image respectively. The output matrix obtained by performing generalized singular value decomposition on a random phase mask; and These represent the diagonal matrices obtained by generalized singular value decomposition. The key is obtained by performing phase-truncation and amplitude-truncation Fourier transforms. and the middle ciphertext ; They represent the complex matrix of the image respectively. The output matrix obtained by performing generalized singular value decomposition on a random phase mask; Represents a diagonal matrix The key is obtained by performing an amplitude-trunculated inverse Fourier transform. This represents the operation of fetching the imaginary part; Represents the operation of taking the real part; The representative passed the cipher. Generate the first The predicted blue component of the original image in the next iteration; The representative passed the cipher. Generate the first The intermediate matrix of the next iteration; and These represent the predicted values ​​of the red and green components of the original image, generated based on the previously generated key, respectively.

[0116] Figure 10 In the middle: the horizontal axis represents the number of iterations; the vertical axis is a curve showing the correlation coefficient between the decrypted image recovered through the special attack and the original image as a function of the number of iterations.

[0117] Figure 11 This is a schematic diagram illustrating the working principle of the present invention. Detailed Implementation

[0118] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] Please see Figure 1-11 This invention provides a technical solution: an asymmetric color image optical encryption method based on generalized singular value decomposition, comprising an encryption process and a decryption process.

[0120] 1) Encryption process: The color image is first encoded into a complex matrix. The resulting complex matrix is ​​modulated with a phase plate using generalized singular value decomposition. Then, phase truncation is applied in the optical Fourier transform domain for encryption. Finally, the ciphertext is received through a charge-coupled device (CCD). The encryption process of the encryption algorithm is described below:

[0121] Step 1: Assume the image needs to be encrypted. For a picture of size For a pixel-based color image, the three color components of the image are first normalized. , , These represent the normalized red, green, and blue color components, respectively. Then, the red and green components are used as the real and imaginary parts of the complex number, respectively, to encode the first complex matrix. :

[0122]

[0123] Step 2: Convert the first complex matrix With the first random phase mask Generalized singular value decomposition yields two unitary matrices. and A square array and two non-negative diagonal matrices and :

[0124]

[0125] Step 3: For non-negative diagonal matrices Perform a Fourier transform to obtain the matrix in the frequency domain. :

[0126]

[0127] Step 4: In the frequency domain, for Perform phase truncation and amplitude truncation:

[0128]

[0129]

[0130] in, and These respectively indicate phase truncation and amplitude truncation.

[0131] Step 5: Amplitude information obtained after phase truncation The blue component of the image is encoded as the real and imaginary parts of the complex number, respectively, into a second complex matrix. :

[0132]

[0133] Step 6: For the second complex matrix Second random phase mask Perform generalized singular value decomposition:

[0134]

[0135] Step 7: For non-negative diagonal matrices The spatial domain image is obtained by performing an inverse Fourier transform. :

[0136]

[0137] Step 8: Perform phase and amplitude truncation on it in the spatial domain:

[0138]

[0139]

[0140] Step 9: Amplitude information obtained after phase truncation Transmitted as encrypted text;

[0141] Two random phase masks were used in the encryption process. and Two square matrices generated during the encryption process and Two unitary matrices and The phase information matrix obtained by two amplitude truncations and Both are used as decryption keys to decrypt the images;

[0142] 2) Decryption process: First, the matrix is ​​recovered using the ciphertext and private key. Then, a Fourier transform is performed on the matrix to obtain the next matrix. The matrix is ​​then recovered based on the principle of generalized singular value decomposition. Finally, the blue component of the original image and the matrix are extracted from the imaginary and real parts of the complex matrix. The decryption process of the encryption algorithm is described below:

[0143] Step 1: Decryption begins with the ciphertext. and private key Recovery Matrix :

[0144]

[0145] in Represents matrix dot product;

[0146] Step 2: For the matrix The matrix is ​​obtained by performing a Fourier transform. :

[0147]

[0148] Step 3: Recover the second complex matrix based on the principle of generalized singular value decomposition. :

[0149]

[0150] in, Representation matrix The conjugate transpose of ;

[0151] Step 4: From the second complex matrix Extracting the blue component from the imaginary and real parts of the original image sum matrix :

[0152]

[0153]

[0154] here, This indicates extracting the imaginary part of a complex number. This indicates extracting the real part of a complex number;

[0155] Step 5: Using the private key Recovery Matrix :

[0156]

[0157] Step 6: For the matrix The matrix is ​​obtained by performing an inverse Fourier transform. :

[0158]

[0159] Step 7: Recover the complex matrix based on the principle of generalized singular value decomposition. :

[0160]

[0161] Step 8: Extracting the real and imaginary parts will recover the red component of the original image. and green components :

[0162]

[0163]

[0164] The encryption system uses a random phase mask. and Encryption, using , , , , and The encrypted text is decrypted because the encryption key and the decryption key are different, thus achieving asymmetric encryption. In addition, the encryption system can also be used to encrypt three grayscale images simultaneously. By using three grayscale images to replace the three color components of the color image for encryption, three grayscale images can be encrypted simultaneously.

[0165] The matrix is ​​then recovered using the private key, and an inverse Fourier transform is performed on the matrix to obtain the next matrix. The complex matrix is ​​then recovered based on the principle of generalized singular value decomposition. The real and imaginary parts are extracted to recover the red and green components of the original image. The original image can then be recovered from the extracted blue, red, and green components.

[0166] The specific steps of the attack based on iterative recovery designed in this invention are detailed as follows:

[0167] matrix , , The first generation generated by the amplitude-phase retrieval algorithm The predicted values ​​represent the red, green, and blue components of the image, respectively. When performing the first iteration, its initial value is set to 1; matrix This is encrypted text used to constrain the recovered image;

[0168] Step 1: First, perform generalized singular value decomposition on the image complex matrix and the random phase mask:

[0169]

[0170] Step 2: Obtain the diagonal matrix from the generalized singular value decomposition. The key is obtained by performing phase-truncation and amplitude-truncation Fourier transforms. and the middle ciphertext :

[0171]

[0172]

[0173] Step 3: Convert the matrix The predicted value of the blue component of the original image The real and imaginary parts of the complex number are encoded into a complex matrix, respectively. Then, this complex matrix and a random phase mask are used... Perform generalized singular value decomposition:

[0174]

[0175] Step 4: Divide the diagonal matrix The key is obtained by performing an amplitude-trunculated inverse Fourier transform. :

[0176]

[0177] Step 5: Through ciphertext Generate the first Predicted blue component values ​​of the original image in the next iteration:

[0178]

[0179] Step 6: Generate intermediate matrix :

[0180]

[0181] Step 7: Generate predicted values ​​for the color matrix of the original image based on the previously generated key:

[0182]

[0183] Step 8: Extracting the real and imaginary parts separately yields the predicted values ​​of the red and green components of the original image.

[0184]

[0185] .

[0186] Please see Figure 1-2 As shown, an asymmetric color image optical encryption and decryption method based on generalized singular value decomposition is presented. To verify the effectiveness and robustness of the method, Figure 3-8 Experimental results for encrypting and decrypting an input color image are presented;

[0187] Please see Figure 1-2 As shown, an asymmetric color image optical encryption and decryption method based on generalized singular value decomposition is presented. To verify the effectiveness and robustness of the method, Figure 3-8 Experimental results for encrypting and decrypting an input color image are presented:

[0188] Figure 1 The encryption process of the proposed encryption algorithm uses the red component of the original color image. and green components The real and imaginary parts of a complex number are encoded into a complex matrix. The complex matrix and the random phase mask Generalized singular value decomposition yields two unitary matrices. and A square array and two non-negative diagonal matrices and For non-negative diagonal matrices Perform a Fourier transform to obtain the matrix in the frequency domain. The next step is in the frequency domain, for Phase truncation and amplitude truncation are performed; amplitude information is obtained after phase truncation. The blue component of the image is used as the real and imaginary parts of the complex number, respectively, to encode a complex matrix. For complex matrices and random phase mask The two unitary matrices obtained by generalized singular value decomposition and A square array and two non-negative diagonal matrices and For non-negative diagonal matrices The spatial domain image is obtained by performing an inverse Fourier transform. In the spatial domain, phase and amplitude are truncated, and the amplitude information obtained after phase truncation is... As encrypted transmission; two random phase masks were used in the encryption process. and Two square matrices generated during the encryption process and Two unitary matrices and The phase information matrix obtained by two amplitude truncations and Used as a decryption key to decrypt the image;

[0189] Figure 2 The decryption process of the proposed encryption algorithm first involves using the ciphertext... and private key Recovery Matrix Then, for the matrix The matrix is ​​obtained by performing a Fourier transform. Then, the matrix is ​​recovered based on the principle of generalized singular value decomposition. From complex matrices Extracting the blue component from the imaginary and real parts of the original image sum matrix Use private key Recovery Matrix Then, for the matrix The matrix is ​​obtained by performing an inverse Fourier transform. Then, based on the principle of generalized singular value decomposition, the complex matrix can be recovered. The red component of the original image can be recovered by extracting its real and imaginary parts. and green components ; from the extracted blue component Red component and green components The original image can then be recovered. The encryption system uses a random phase mask. and Encryption, using , , , , and The encrypted text is decrypted because the encryption key and the decryption key are different, thus achieving asymmetric encryption. In addition, the encryption system can also be used to encrypt three grayscale images simultaneously. By using three grayscale images to replace the three color components of the color image for encryption, three grayscale images can be encrypted simultaneously.

[0190] Figure 3 (a) is the original color image to be encrypted, and the resulting grayscale encrypted image after being encrypted using the proposed encryption algorithm. Figure 3 As shown in (b); by Figure 3 (b) It can be seen that the information in the color image is encrypted. When all keys are correct and the image is not attacked, all the information in the color image can be completely restored to obtain the original image (e.g., ...). Figure 3 (c) shows that the encryption and decryption of color images using this system is successful;

[0191] Figure 4 (a) is the original Figure 3 Figure (a) shows the histogram distribution, and Figure (b) shows the histogram distribution after encryption. Figure 3 (b) Histogram distribution; By comparison, it can be seen that the peak value and histogram distribution of the ciphertext and the original image are completely different. Therefore, it is impossible to obtain any effective information about the original image by analyzing the histogram distribution of the ciphertext.

[0192] Furthermore, when one key is incorrect while the others are correct, the decryption result of the color image is as follows: Figure 5 As shown in (a)-5(f), it can be seen that the security of this encryption system can be guaranteed.

[0193] Figure 6 (a) is the ciphertext with 1 / 64 cut. Figure 6 (b) is its corresponding decrypted image. Figure 6 (c) is the ciphertext with 1 / 16 cut. Figure 6 (d) is the corresponding decrypted image. The cut area is marked for easy observation. It can be seen from the decrypted image that after being subjected to a cut attack, there is a lot of noise in the decrypted image, but the main information of the image can still be distinguished. Therefore, the encryption method proposed in this invention can resist cut attacks.

[0194] Figure 7 Images decrypted under Gaussian random noise interference at different noise intensity coefficients; Figure 7 (a), Figure 7 (b), Figure 7(c) shows the noise intensity coefficients of 0.1, 0.2, and 0.5 respectively; it can be seen from the decrypted images that the stronger the noise, the more severe the interference with the decrypted image; however, the main information of the original image can still be distinguished, thus proving that the encryption method proposed in this invention can resist noise attacks;

[0195] It is evident that even if the encrypted image is heavily contaminated by noise or partially missing information, the present invention can still decrypt the original color image that can be identified, verifying the feasibility of the system and meeting various needs in practical applications.

[0196] Figure 8 To select the results of the plaintext attack test; assuming the attacker already knows the ciphertext and the entire encryption process, the attacker encrypts pseudo-plaintext. Figure 8 (a) Obtaining a fake key; the attacker then uses the fake key to decrypt the ciphertext. Figure 3 (b) The decrypted image is shown in 8(b). As can be seen from the attack, the decrypted image does not contain any information from the original image 3(a) that was attacked, but only contains part of the pseudo-plaintext information. By calculation, the correlation coefficient between the decrypted image and the original image that was attacked is 0.0975, which proves that the encryption method can resist chosen-plaintext attacks.

[0197] Please see Figure 9-10 As shown, a special attack based on iterative recovery designed against this invention and the corresponding experimental results are presented:

[0198] Figure 9 To counter this invention, a special attack process based on iterative recovery was designed, and the matrix... , , The first generation generated by the amplitude-phase retrieval algorithm The predicted values ​​represent the red, green, and blue components of the image, respectively. When performing the first iteration, its initial value is set to 1; matrix This is encrypted and used to constrain the recovered image; the process of the special attack will be explained in detail below; first, generalized singular value decomposition is performed on the image complex matrix and the random phase mask, and the diagonal matrix obtained from the generalized singular value decomposition is... The key is obtained by performing phase-truncation and amplitude-truncation Fourier transforms. and the middle ciphertext ; to matrix The predicted value of the blue component of the original image The real and imaginary parts of the complex number are encoded into a complex matrix, respectively. Then, this complex matrix and a random phase mask are used... Perform generalized singular value decomposition on the diagonal matrix. The key is obtained by performing an amplitude-trunculated inverse Fourier transform. Through ciphertext Generate the first The blue component prediction values ​​of the original image in the next iteration are then used to generate the intermediate matrix. Based on the previously generated key, the predicted value of the color matrix of the original image is generated. The predicted values ​​of the red and green components of the original image can be obtained by extracting the real and imaginary parts respectively.

[0199] Figure 10 The results of a special attack against the encryption method designed in this invention; a special attack with 100 iterations is performed on the encryption method proposed in this invention. Figure 10 (a) is the image recovered after a special attack. Figure 10 (b) A graph showing the correlation coefficient between the decrypted image recovered by the special attack and the original image as a function of the number of iterations. It can be seen that the image recovered after 100 iterations does not contain any information related to the original image. According to 10(b), the correlation coefficient converges and stabilizes at 0.0279. A correlation coefficient of 0.0279 indicates that the correlation between the recovered image and the original image is extremely low. The convergence and stabilization of the correlation coefficient indicates that the correlation coefficient does not change with the number of iterations, indicating that even if the iteration is repeated many times, more relevant information of the original image cannot be recovered. Therefore, it can be proven that the encryption method proposed in this invention can resist special attacks based on iterative recovery.

[0200] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0201] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An asymmetric color image optical encryption method based on generalized singular value decomposition, comprising an encryption process and a decryption process, characterized in that: Encryption process: The color image is first encoded into a complex matrix. The resulting complex matrix is ​​modulated with a phase plate using generalized singular value decomposition. Then, phase truncation is applied in the optical Fourier transform domain for encryption. Finally, the ciphertext is received through a charge-coupled device (CCD). The encryption process is described as follows: Step 1: Assume the image needs to be encrypted. For a picture of size For a pixel-based color image, the three color components of the image are first normalized. , , These represent the normalized red, green, and blue color components, respectively. Then, the red and green components are used as the real and imaginary parts of the complex number, respectively, to encode the first complex matrix. : Step 2: Convert the first complex matrix With the first random phase mask Generalized singular value decomposition yields two unitary matrices. and A square array and two non-negative diagonal matrices and : Step 3: For non-negative diagonal matrices Perform a Fourier transform to obtain the matrix in the frequency domain. : Step 4: In the frequency domain, for Perform phase truncation and amplitude truncation: wherein and denote phase truncation and amplitude truncation, respectively; Step 5: Amplitude information obtained after phase truncation The blue component of the image is encoded as the real and imaginary parts of the complex number, respectively, into a second complex matrix. : Step 6: Applying the second complex matrix and the second random phase mask performing a generalized singular value decomposition: Step 7: Diagonalization of non-negative diagonal matrix Inverse Fourier transform to get spatial image : Step 8: Perform phase and amplitude truncation on it in the spatial domain: Step 9: Phase truncated resulting amplitude information As ciphertext transmission; Two random phase masks were used in the encryption process. and Two square matrices generated during the encryption process and Two unitary matrices and The phase information matrix obtained by two amplitude truncations and Both are used as decryption keys to decrypt images; The decryption process described in the encryption process is as follows: Step 1: Decryption starts by recovering the matrix and the private key from the ciphertext : wherein denotes a matrix point multiplication; Step 2: Fourier transform of matrix to obtain matrix : Step 3: Recovering the second complex matrix according to the principle of generalized singular value decomposition : in, Representation matrix The conjugate transpose of ; Step 4: From the second complex matrix Extracting the blue component from the imaginary and real parts of the original image sum matrix : here, This indicates extracting the imaginary part of a complex number. This indicates extracting the real part of a complex number; Step 5: Use private key Recovery matrix : Step 6: Inverse Fourier transform of matrix results in matrix : Step 7: Recover the first complex matrix according to the principle of generalized singular value decomposition : Step 8: Extracting the real and imaginary parts will recover the red component of the original image. and green components : The original image can be recovered from the extracted blue, red, and green components; This encryption method can also be used to encrypt three grayscale images simultaneously. By using three grayscale images instead of the three color components of a color image for encryption, three grayscale images can be encrypted at the same time.

2. The asymmetric color image optical encryption method based on generalized singular value decomposition according to claim 1, targeting a special attack based on iterative recovery, is detailed as follows: matrix , , The first generation generated by the amplitude-phase retrieval algorithm The predicted values ​​represent the red, green, and blue components of the image, respectively. When performing the first iteration, its initial value is set to 1; matrix This is encrypted text used to constrain the recovered image; Step 1: First, perform generalized singular value decomposition on the image complex matrix and the random phase mask: Step 2: Obtain the diagonal matrix from the generalized singular value decomposition. The key is obtained by performing phase-truncation and amplitude-truncation Fourier transforms. and the middle ciphertext : Step 3: Convert the matrix The predicted value of the blue component of the original image The real and imaginary parts of the complex number are encoded into a complex matrix, respectively. Then, this complex matrix and a random phase mask are used... Perform generalized singular value decomposition: Step 4: Divide the diagonal matrix The key is obtained by performing an amplitude-trunculated inverse Fourier transform. : Step 5: by the ciphertext generate the first iteration of the original image blue component prediction value: Step 6: Generate intermediate matrix : Step 7: Generate predicted values ​​for the color matrix of the original image based on the previously generated key: Step 8: Extracting the real and imaginary parts separately yields the predicted values ​​of the red and green components of the original image. 。

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